If you see constant [Trial Expired] message in Neutron please check the version of Google Play Store app in OS settings -> Apps -> Google Play Store. If it is 10.7.17 then License verification is broken in this version and you need to wait until OTA update of the Google Play Store or force install it manually from archive in APK Mirror:

Yes. That's right, it's Google's mistake. When I try to install over the Google version of the version I downloaded from the site, it showed me new permissions for the application, namely "account search", there is no access to them in the Google version.

If you downloaded from PayPro's section, that apk will require permission to access accounts in order to find purchase in the license database which is always bound to the e-mail account. For Google Play purchased Neutron it is not needed though because license is checked via Google Play Store's app, so if you dislike this permission download from the Google Play only section.